Question

In the given figure shows a toy. Its lower part is a hemisphere and the upper part is a cone. Find the volume and surface area of the toy from the measures shown in the figure (\[\pi = 3 . 14\])

Answer 1

Radius of the hemisphere = Radius of the cone = r = 3 cm
Height of the cone, h = 4 cm
Let l be the slant height of the cone. 

\[l = \sqrt{r^2 + h^2} = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5 cm\]

Volume of cone = `1/3 pi "r"^2 "h"`

`= 1/3 xx pi xx 3^2 xx 4`

`= 12 pi "cm"^3`

Curved surface area of cone = `pi"rl"`

`= pi xx 3 xx 5 = 15 pi "cm"^2`

Volume of hemisphere = `2/3 pi"r"^3`

`= 2/3 xx pi xx 3^3`

`= 18 pi  "cm"^3`

Curved surface area of hemisphere = `2pi"r"^2`

`= 2 xx pi xx 3^2 = 18pi "cm"^2`

Now, volume of the toy = Volume of cone + volume of hemisphere 

= 12π + 18π

= 30π = 30 × 3.14

= 94.20 cm³

Also, surface area of the toy = Curved surface area of cone + Curved surface area of hemisphere

= 15π + 18π

= 33π

= 33 × 3.14

= 103.62 cm2

∴ The volume and surface area of the toy are 94.20 cm³ and 103.62 cm² respectively.